Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.

SECT. II. Of sailing by the true Sea Chart, commonly called MERCATOR'S Chart.

THE true Sea Chart, commonly called MERCATOR'S Chart* 1.1, performs the same Conclusions as the Plain Chart, and almost as speedily, but far more exactly: Because all Pla∣ces may be laid down hereon, with the same truth as on the Globe it self: both to their Lati∣tudes, Longitudes, Bearing and Distance from each other.

And here it will be necessary to have a Table of Meridional Ports, which I have extracted out of Mr. Wright's Tables, to every tenth Minute of Latitude; accounting it in single Miles, or Minutes of the Equinoctial, and have hereunto annexed the said Table.

A Table of Meridional Miles

The Deg. of Lat.	The Minutes of each Degree.	The Difference.
0	10	20	30	40	50
The Meridional Miles.
0	0	10	20	30	40	50	10
1	60	70	80	90	100	110	10
2	120	130	140	150	160	170	10
3	180	190	200	210	220	230	10
4	240	250	260	270	280	290	10
5	300	310	320	330	340	350	10
6	360	370	380	390	400	410	10
7	421	431	441	451	461	471	10
8	481	491	501	511	521	532	10
9	542	552	562	572	582	592	10
10	603	613	623	633	643	653	10
11	664	674	684	694	704	715	10
12	725	735	745	755	766	776	10
13	786	797	807	817	827	838	10
14	848	858	869	879	889	900	10
15	910	920	931	941	951	962	10
16	972	983	993	1004	1014	1024	10
17	1035	1045	1056	1066	1077	1087	10
18	1098	1108	1119	1129	1140	1150	10
19	1161	1172	1182	1193	1203	1214	10
20	1225	1235	1246	1257	1267	1278	11
21	1289	1299	1310	1321	1332	1342	11
22	1353	1364	1375	1386	1396	1407	11
23	1418	1429	1440	1451	1462	1473	11
24	1484	1499	1505	1516	1527	1538	11
25	1549	1561	1572	1583	1594	1605	11
26	1616	1627	1638	1649	1661	1672	11
27	1683	1694	1705	1717	1728	1738	11
28	1751	1761	1773	1785	1796	1808	11
29	1819	1830	1842	1853	1865	1867	11

The Deg. of Lat.	The Minutes of each Degree.	The Difference.
0	10	20	30	40	50
The Meridional Miles.
30	1888	1899	1911	1923	1934	1946	12
31	1958	1969	1981	1993	2004	2016	12
32	2028	2040	2052	2063	2075	2087	12
33	2099	2111	2123	2135	2147	2159	12
34	2171	2183	2195	2207	2219	2231	12
35	2244	2256	2268	2281	2293	2305	12
36	2318	2330	2342	2355	2367	2380	12
37	2392	2405	2417	2430	2442	2455	12
38	2468	2481	2493	2506	2519	2532	13
39	2544	2557	2570	2583	2596	2609	13
40	2622	2635	2648	2662	2675	2668	13
41	2701	2714	2718	2741	2754	2768	13
42	2781	2795	2808	2822	2835	2849	13
43	2863	2876	2890	2904	2918	2931	14
44	2945	2959	2973	2987	3001	3015	14
45	3030	3044	3050	3072	3086	3101	14
46	3115	3130	3144	3159	3173	3188	14
47	3202	3217	3232	3247	3261	3276	15
48	3291	3306	3321	3336	3351	3366	15
49	3382	3397	3412	3428	3443	3459	15
50	3474	3490	3505	3521	3537	3553	16
51	3568	3584	3600	3616	3632	3649	16
52	3665	3681	3697	3714	3730	3747	16
53	3763	3780	3797	3814	3830	3847	17
54	3864	3881	3899	3616	3933	3950	17
55	3968	3985	4003	4020	4038	4056	18
56	4074	4092	4110	4128	4146	4164	19
57	4182	4201	4219	4238	4257	4275	19
58	4294	4313	4331	4351	4370	4390	20
59	4409	4428	4448	4468	4487	4507	20

The Deg. of Lat.	The Minutes of each Degree.	The Difference.
0	10	20	30	40	50
The Meridional Miles.
60	4527	4547	4567	4588	4608	4629	20
61	4643	4670	4691	4711	4733	4754	21
62	4775	4796	4818	4839	4861	4883	22
63	4905	4927	4949	4972	4994	5017	23
64	5039	5062	5085	5018	5132	5155	23
65	5179	5203	5226	5250	5275	5299	24
66	5324	5348	5373	5390	5423	5449	25
67	5474	5500	5520	5552	5678	5704	26
68	5631	5658	5685	5712	5739	5767	27
69	5795	5823	6021	5879	5908	5937	28
70	5966	5996	6125	6055	6085	6115	30
71	〈…〉〈…〉	6177	6208	6239	6271	6303	31
72	6335	6368	6401	6431	6468	6501	33
73	6535	6570	6605	6640	6675	6718	35
74	6747	6783	6620	6857	6895	6933	37
75	6972	7010	7050	〈…〉〈…〉	7130	7170	40
76	7211	7253	7295	7338	7381	7424	43
77	7469	7513	7559	7605	7651	7651	7698	46
78	7746	7795	7844	7894	7944	7996	50
79	8048	8100	8154	8209	8264	8320	55
80	8377	8435	8495	8555	8616	8678	60
81	8742	8806	8872	8939	9007	9077	68
82	9148	9221	9295	9371	9449	9523	77
83	9609	9692	9778	9865	9954	〈…〉〈…〉	88
84	10141	10238	〈…〉〈…〉	10441	10547	10656	105
85	10770	10887	11007	11133	〈…〉〈…〉	〈…〉〈…〉	128
86	11539	11686	11839	11999	12168	12344	165
87	12521	12718	〈…〉〈…〉	13150	13388	〈…〉〈…〉	〈◊〉〈◊〉
88	13920	14221	14550	14914	15321	15783	386
89	16318	16950	17726	18729	20152	22623

PROP. I. To find by the Table, what Meridional parts are contained in any Difference of Latitude.

The Use of the Table is demonstrated by the several Examples following, after this Manner.

In this Proposition three Varieties present themselves unto our View.

• 1. When one Place is under the Equinoctial, the other having North, or South Latitude, his Meridional parts corresponding, is to be esteem∣ed for the Meridional Difference of Latitude.
• 2. When both Places are towards one of the Poles, then the Meridional parts of the lesser, taken from the Meridional parts of the greater Latitude, the remainder is the Meridional dif∣ference required.
• 3. When one Place hath North, and the o∣ther South Latitude, their corresponding Me∣ridional parts added together gives the Meridio∣nal difference of Latitude sought: thus having sound them out they may thus be applyed.

PROP. II By knowing the Latitudes, and the difference of Longitude of any two Places, to find the Rumb, and Distance.

Admit there be a Port in the Latitude of 50° 00' North, and another in the Latitude of 13° 12' North, and their Difference of Longitude is 52° 57' West, I demand the Rumb and Di∣stance?

In the Triangle A b c, let A b represent the proper difference of Latitude, bc the Departure, Ac the distance sailed, A the Angle of the* 1.2 Course, c the Complement of the Course.

In the Triangle ABC, AB is the Meridional difference of Latitude, BC the Difference of Lon∣gitude, A the Angle of the Rumb, C the Compl. of the Angle of the Rumb: These things being understood the work evidently appears to be the same as in Rightangled Plain Triangles.

There is then required first the Difference of Latitude, and this falls under the second Va∣riety.〈 math 〉〈 math 〉

1. To find the Rumb or Course say,

As Merid. X. Lat. 2676',

To Radius or S. 90°.

So is X. of Longitude 3177',

To T. of the Rumb 49° 53', the Course there fore is S. W. ½ W, &c.

2. To find the Distance,* 1.3 * 1.4

As Sc. Course 40° 07',

To proper X. of Lat. 2208'.

So is Radius or S. 90°,

To the Distance 3426 Minutes as required.

PROP. III. By knowing the Latitudes, and distance of two Places, to find the Rumb, and Difference of Lon∣gitude.

1. To find the Rumb or Course say,

As the Distance sailed,

To Radius or S. 90°.

So is the X. of Latitude,

To Sc. of the Rumb required.

2. To find the Difference of Longitude say,

As Radius or S. 90°,

To the X. of Latitude in Merid. Parts.

So is T. of the Rumb,

To the X. of Longitude required.

PROP. IV. By knowing the Latitudes, and Rumb of two Pla∣ces, to find their Distance, and Difference of Longitude.

1. To find the Distance say,

As Sc of the Rumb,

To the X of Latitude.

So is Radius or S. 90°,

To the Distance required.

2. To find the Difference of Longitude say,

As Radius or S. 90°,

To the X. of Latitude in M. Parts.

So is T. of the Rumb,

To the X. of Longitude required.

PROP. V. By knowing the Rumb, Difference of Longitude, and one Latitude, to find the other Latitude, and the Distance.

1. To find the other Latitude say,

As T. of the Rumb,

To the X of Longitude in parts.

So is Radius or S. 90°,

To the Merid. X. of Latitude required.

2. To find the Distance say,

As Sc. of the Rumb,

To the X. of Latitude.

So is Radius or S. 90°,

To the required Distance,

PROP. VI. By knowing the Distance, one Latitude, and Rumb, to find the other Latitude, and Difference of Longitude.

1. To find the Difference of Latitude say,

As Radius or S. 90°,

To the Distance.

So is Sc. of the Rumb,

To the X. of Latitude required.

2. To find the Difference of Longitude say,

As Radius or S. 90°,

To the Merid. X. of Latitude.

So is T. of the Rumb,

To the X. of the Longitude required.

Notes

• * 1.1

  But is indeed the In∣vention of our Learned Countryman Mr. Edw. Wright, although this Stranger hath almost got the Name and Praise thereof.
• * 1.2

  Fig. 50.
• * 1.3

  Fig. 50.
• * 1.4

  〈 math 〉〈 math 〉